Quantitative study of semi-Pfaffian sets
Algebraic Geometry
2007-05-23 v1 Logic
Abstract
We study the topological complexity of sets defined using Khovanskii's Pfaffian functions, in terms of an appropriate notion of format for those sets. We consider semi- and sub-Pfaffian sets, but more generally any definable set in the o-minimal structure generated by the Pfaffian functions, using the construction of that structure via Gabrielov's notion of limit sets. All the results revolve around giving effective upper-bounds on the Betti numbers (for the singular homology) of those sets. Keywords: Pfaffian functions, fewnomials, o-minimal structures, tame topology, spectral sequences, Morse theory.
Cite
@article{arxiv.math/0401079,
title = {Quantitative study of semi-Pfaffian sets},
author = {Thierry Zell},
journal= {arXiv preprint arXiv:math/0401079},
year = {2007}
}
Comments
Author's PhD thesis. Approx. 130 pages, no figures